Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods: 94 (Probability Theory and Stochastic Modelling, 94) - Tapa dura

Libro 27 de 34: Probability Theory and Stochastic Modelling

Budhiraja, Amarjit; Dupuis, Paul

 
9781493995776: Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods: 94 (Probability Theory and Stochastic Modelling, 94)
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ISBN 10: 1493995774 ISBN 13: 9781493995776
Editorial: Springer, 2019

Sinopsis

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values.  By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation.  The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.


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Acerca del autor

Amarjit Budhiraja is a Professor of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He is a Fellow of the IMS. His research interests include stochastic analysis, the theory of large deviations, stochastic networks and stochastic nonlinear filtering.​
Paul Dupuis is the IBM Professor of Applied Mathematics at Brown University and a Fellow of the AMS, SIAM and IMS.  His research interests include stochastic control, the theory of large deviations and numerical methods.

De la contraportada

This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values.  By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations.  These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values.  This connection is illustrated through thedesign and analysis of importance sampling and splitting schemes for rare event estimation.  The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.

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Editorial
Springer
Año de publicación
2019
Idioma
Inglés
ISBN 10 
1493995774
ISBN 13 
9781493995776
Encuadernación
Tapa dura
Número de edición
1
Número de páginas
596
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Otras ediciones populares con el mismo título

9781493996223: Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods: 94 (Probability Theory and Stochastic Modelling)

Edición Destacada

ISBN 10:  1493996223 ISBN 13:  9781493996223
Editorial: Springer, 2020
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